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3 years ago

The sum of three consecutive even integers is –78. What are the integers?

1 answer:

6 0

You need to write 3 consecutive EVEN numbers using only one variable. multiply by 2 to ensure the numbers are even. Add or subtract 2 to get the next consecutive number.
(2x - 2) , (2x) , (2x + 2)

add them up to equal -78
-78 = (2x-2) + 2x + (2x+2)
-78 = 6x
-78/6 = x
-13 = x

the numbers are: (2(-13)-2) , 2(-13) , (2(-13)+2)
-28, -26 , -24

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Help me please. <br>Help me please. <br>Help me please.

Gnesinka [82]

A)
To be similar triangles have to have equal angles
triangle ZDB'
1)angle Z=90 degrees
triangle B'CQ
1) angle C 90 degrees

angle A'B'Q=90
DB'Z+A'B'Q+CB'Q=180, straight angle
DB'Z+90+CB'Q=180
DB'Z+CB'Q=90

triangle ZDB'
DZB'+DB'Z=180-90=90

DB'Z+CB'Q=90
DZB'+DB'Z=90
DB'Z+CB'Q=DZB'+DB'Z
2)CB'Q=DZB' (these angles from two triangles ZDB' and B'CQ )
3)so,angles DB'Z and B'QC are going to be equal because of sum of three angles in triangles =180 degrees and 2 angles already equal.
so this triangles are similar by tree angles
b)
B'C:B'D=3:4
B'D:DZ=3:2
CQ-?
DC=AB=21
DC=B'C+B'D (3+4= 7 parts)
21/7=3
B'C=3*3=9
B'D=3*4=12
B'D:DZ=3:2
12:DZ=3:2
DZ=12*2/3=8
B'D:DZ=CQ:B'C
3:2=CQ:9
CQ=3*9/2=27/2

c)
BC=BQ+QC=B'Q+QC
BQ' can be found by pythagorean theorem

3 0

3 years ago

How to factor completely 2x^2+19x+24

Gnom [1K]

2=2*1,1*2
24=1*24,2*12,6*4,3*8
19=2*8+3

2x²+19x+24
(2x+3)(x+8)

or
2x(x+8)+3(x+8)
2x²+16x+3x+24
2x²+19x+24

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3 years ago

3 + root 3 *2 +root 2

icang [17]

Answer:

6 + 3 $\sqrt{2}$ + 2 $\sqrt{3}$ + $\sqrt{6}$

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Given

(3 + $\sqrt{3}$ )(2 + $\sqrt{2}$ )

Each term in the second factor is multiplied by each term in the first factor, that is

3(2 + $\sqrt{2}$ ) + $\sqrt{3}$ (2 + $\sqrt{2}$ ) ← distribute both parenthesis

= 6 + 3 $\sqrt{2}$ + 2 $\sqrt{3}$ + $\sqrt{6}$

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3 years ago

Praying someone answers this

Alekssandra [29.7K]

The building is 24 (whatever’s you want ex. Meters, Feet) high. Because 38.7=tan^-1(height/30). Or cos(38.7)=30/hypotenuse. Hypotenuse=30/cos(38.7

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3 years ago

An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartr

Basile [38]

Answer / Step-by-step explanation:

In this exercise, we know that the agency collected 1,829 bullets which according to the agency, all came from different source.

The number of pair of bullet is :

(1,829) = 1, 829 ! / 2! ( 1,829 - 2 ) = 1, 829 x 1,828 x 1827 ! / 2 x 1 x 1,827

( 2 )

= 6, 108,413,724 / 3654

= 1671,706.

Also, we know that the agency found 658 matches. According to this, the chance of false positive ( that is, the agencies find a match but the bullets are from two different source ) is

P (False positive ) = 658 / 671,706

= 0.000979.

The probability is small to an extent, therefore, we should have confidence in the agency forensic report and evidence

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3 years ago